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arXiv · 2107.12805

Whitehead algorithm for automorphisms of generalized Baumslag-Solitar groups

Chloé Papin
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Abstract

In analogy with the free factors of a free group we define special factors of Generalized Baumslag-Solitar (GBS) groups as non-cyclic subgroups which appear in splittings over infinite cyclic groups. We give an algorithm which, given a GBS group $G$ and an element $g \in G$, decides whether there exists a special factor $H < G$ such that $g \in H$. This algorithm is analogous to an algorithm by Whitehead for free groups. Furthermore we prove that given $g \in G$ there exists a unique minimal special factor containing $g$ and give an algorithm which finds it.

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Chloé Papin. 2021-07-27. Whitehead algorithm for automorphisms of generalized Baumslag-Solitar groups. https://arxiv.org/abs/2107.12805

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